Question: Simplify. Multiply and remove all perfect squares from inside the square roots. Assume $a$ is positive. $\sqrt{2a}\cdot\sqrt{14a^3}\cdot\sqrt{5a}=$
Solution: Let's start by merging the square roots: $\begin{aligned} \sqrt{2a}\cdot\sqrt{14a^3}\cdot\sqrt{5a} &=\sqrt{2a\cdot 14a^3\cdot 5a} \\\\ &=\sqrt{140a^5} \end{aligned}$ Now we remove all perfect squares from inside the square root: $\begin{aligned} \sqrt{140a^5} &=\sqrt{2^2\cdot 5\cdot 7\cdot \left(a^2\right)^2\cdot a} \\\\ &=\sqrt{2^2}\cdot\sqrt{35}\cdot\sqrt{ \left(a^2\right)^2}\cdot \sqrt{a} \\\\ &=2\cdot \sqrt{35}\cdot a^2\cdot \sqrt{a} \\\\ &=2a^2\sqrt{35a} \end{aligned}$ In conclusion, $\sqrt{2a}\cdot\sqrt{14a^3}\cdot\sqrt{5a}=2a^2\sqrt{35a}$